Week 16.10.2023 – 22.10.2023

In these lectures we will provide a basic introduction to Supergravity as it arises in String Theory and M-Theory. We will start by introducing vielbeins and spin connections in order to construct supergravity actions. In the second lecture we will briefly introduce the maximal supergravity theories in ten and eleven-dimensions. We will briefly discuss special holonomy manifolds, explicitly construct BPS p-brane solutions and prove their non-perturbative stability. Time permitting we will discuss toroidal compactifications and U-duality. I will assume basic MSc level material (Riemannian geometry, fermions and rigid supersymmetry). The lecture notes that will be provided are largely self-contained but the text book “Supergravity” by Freedman and van Proeyen contains more details.

We discuss two notions of entanglement of internal degrees of freedom. The first notion is target space entanglement: we show how to define entanglement of matrix degrees of freedom in a gauge invariant manner, and discuss connections to holography. The second notion relates to global symmetries in AdS/CFT settings and relates to an interpretation of Ryu-Takayanagi surfaces which are anchored on the boundary of a subregion on the internal space and smeared in the AdS spatial directions.

The Symmetry Topological field theory (SymTFT) has played an important role in recent studies of symmetries in physics. As one application, it provides a clear and unifying picture of bosonization and fermionization in two dimensions. On the other hand, for theories having a non-anomalous Z_N symmetry with N > 2, people have long speculated about the presence of parafermions. In this informal talk, we revisit the bosonization/parafermionization procedure from the SymTFT point of view, and explain some subtleties and peculiarities involved. It will be based on 2309.01913 and (hopefully) accessible to a broad audience. Part of the London TQFT journal club (https://www.london-tqft.co.uk)

I'll discuss recent results on line and surface defects in the N=4 Super-Yang-Mills (SYM) beyond perturbation theory. In addition to providing new observables in the SYM that capture the gauge theory dynamics in the presence of impurities, these non-perturbative results detect the nontrivial SL(2,Z) structure and provide an exact order parameter for the deconfinement phase transition. Furthermore, via AdS/CFT, they lead to novel predictions for the world-volume action of branes in type IIB string theory at finite string coupling and present a new perspective on the Hawking-Page transition for black holes in AdS.

We discuss numerical results from integrability for the Hagedorn temperature in N=4 SYM and ABJM theory at strong coupling and compare them to the Hagedorn temperatures of their string theory duals. From the numerics we conjecture the leading analytic coefficients in the expansion about large 't Hooft coupling. This talk is based on arXiv:2306.09883 and arXiv:2307.02350.